Transcript A Hybrid Spin-down Model and Its Application to the Isolated

Probe into Magnetic Field
and Initial Period of
Neutron Star
Basis

Two models

72 Pulsars data with transverse
velocities( form Dr Wang, possible recycle
pulsars are deducted)
Superfluid Vortex of NS
Vortex flow
Vortex core
(normal neutrons)
Spin-down by neutrino radiation from
superfluid vortex (Basic theory: Peng et al.1982)



It is general believed that neutron superfluid in the interior of neutron
stars is in a vortex state, and the vortex lines are parallel to the rotation
axis of the neutron star.
The circularly moved neutrons may emit neutrino pairs owning to the
weak interaction of the neutral current.
Radiation power: the superfluid neutrons plus normal neutrons
Wv  BG(n)
G(n)  n7 / n B  1.0 1057 (8 /  2/ 3 )Rs 3
n is the vortex quantum number;  is the energy gap caused by the
interaction of attraction of the 1S0 wave between neutrons.

Rotation energy of the neutron star keeps infusing to the supfluid
vortices via “Ekman pump mechanism”.
Hybrid model



Rotation energy loss rate:
Period derivative:
Assumptions:

Magnetic field:
Age:

Braking index:

(Dipole model+Superfluid)
(n decreases with increased P)
Contrast between the two models
items
Hybrid Model
Period
derivative
Magnetic
field
Age
Braking
index
 3 n  3
Dipole Model
The observed kick velocities for Pulsars
V(km/s)
Number
Percentage

100
71
75%

300
36
38%

500
14
15%
 1000
5
5%
Parity violation
Ji
J
Jf

p

n
J i  J  J f
n
Neutrino Jet Rocket Model
If the neutron angular momentum is carried away mainly by
neutrinos, the direction of emitted neutrinos with left hand
spin must be opposite to the original neutron angular
momentum , while the neutron itself will get a recoil along
its angular momentum direction.
On the contrary, If the neutron angular momentum is
carried away mainly by the anti-neutrinos, the direction of
the emitted anti-neutrinos with right hand spin must be
the same as the original neutron angular momentum
direction , while the neutron itself will get a recoil
opposite to its angular momentum direction.
Formulae
W
dV
M
 
dt
c
 :Asymmetry factor
2
CG
(
n
)
B
dP

0
12
V   
P0
McA0 ( P )  (1  B G (n ) B  2 ) P 3 P 3 
0
0
12
0
P0
P
72 Pulsars’ B12 and P0


According to upwards models, we calculate
72 Pulsars’ B12 and P0 ,here we choose
=3.0 to simplify solving the non-linear
equations, and  closed 3 makes for
acceleration.
For each pulsar, we choose least n0 make
equation solved.
Calculation Results
P0 min=0.000423s
( B12 =2.832, n0=950 V=2500km/s)
B12 max=27.558
(P0 =0.00057s, n0=1115,V=252km/s )
2) Hybrid Model can reduce magnetic field calculated by
Dipole Model effectively.
n0 max=1325
(B12=11.725,P0=0.000433s, V=1730km/s)
P0
P0_n0
0.006
0.005
0.004
0.003
0.002
0.001
200
B12
400
600
800
B12_n0
20
15
15
10
10
5
5
400
600
1200
P0
20
200
1000
800
1000
1200
n0
B12_P0
n0
0.001
0.002
0.003
0.004
0.005
0.006
B12
Statistics and Fit
n0
Log
B12
P0
Correlation
coefficient:0.882565
_Log n0
7
6.5
6
5.5
6
8
10
Log B12 P0
B12
ln n0  0.264 ln(
)  4.312
P0
Physics Signification


The B12 is higher, that is said, the
presupernova collapsed more fiercely, so
the interior overfall is more disordered, it
can be anticipated n0 is larger.
If P0 increased,because of angular
momentum conversation law,we can draw
same conclusion.
Conclusion and Discussion
1) Neutrino Jet Rocket Model is a gradual
acceleration model, main accelerating
period : P  0.5 s, Vmax  1000 km/s
3)Use the connection of B12-n0-P0, maybe
solve the problem of high magnetic field
and calculate more pulsars’ velocities etc.
4)More work should be done about making
certain involved parameter more
reasonably.
Thank you!